Asked by anonymous
Find the values of p that have ∫[0,1] 1/(x)^p dx and write it as an interval.
Answers
Answered by
oobleck
p must be less than 1
since ∫1/(x)^p dx = ∫[0,1] (x)^-p dx = 1/(1-p) x^(1-p)
and the value at x=0 is undefined
since ∫1/(x)^p dx = ∫[0,1] (x)^-p dx = 1/(1-p) x^(1-p)
and the value at x=0 is undefined
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